How can I retain the data from the existing TM backup but delete those few crucial bits of data that I need securely wiped? My first thought is to copy the contents of the existing TM drive (entirely) to a new external HDD before then formatting (disk erase) my existing TM drive and copying everything back to it except for the files I want deleted... Is this a reliable way that I can retain my original data but delete the sensitive stuff I need deleted?? When I try to securely delete the copied TM data that was moved to the second external HDD will I still encounter that same error that prevented deleting it from my existing TM backup drive? Or is there something about the original TM drive being a "designated" TM backup drive that has put those data deletion blocks in place that I won't encounter by moving the TM data to a non TM drive so I can delete it securely?
They aren't files. You cannot treat them as files. Imagine a basket full of chains. At one end is a link named NOW, and at the other end is ORIGINAL. Between them is a chain, going from Original to version 2 to version 3 to version 4 to....to now. If there is no change, it's a chain of simple links, but occasionally in the chain you get to a full document that was changed from the previous version, so got saved completely. It has links to the previous version, one link at at a time. To get to the original, the system pulls on the chain link-by-link until the original appears, passing all the versions on the way. But the basket has thousands of chains, all tangled together. Break one chain by touching a link and the entire basket of links can fall apart. That's what you are facing. Every time TM made a backup it added a link to the chain. That is the magic of TM, how it can keep years worth of backups and not consume huge storage. Unchanged things get a small link, changed things get a big blob and links going both ways. But the tradeoff is you cannot muck about with the links, it has to be done through TM. You can delete an entire backup, inside TM, but you cannot delete a single FILE in the backup stack. And just to make it more interesting, if a Folder has no changes to any files in it, TM creates a link for the entire Folder, not for the files in it. So, you might chase a chain down link by link for a file, but if it is in a Folder where nothing happens for a few iterations of backup, the link changes from the file to the folder.
You cannot copy everything BUT something from the chains. That is the same a erasing them and breaking the chain. It is simply impossible.
You ask, can you delete the sensitive stuff but keep everything else? Not if you want history. If you don't care about history, just wipe the drive and start over, or better yet, destroy the drive. Or you can delete an entire backup from the middle from inside TM to erase that entire day. TM will rebuild links to cover the gap when you tell it to delete that backup. But if you want to delete ONE file, you cannot do it. TM doesn't have that capability, and if you try to break the chain, you could lose the entire backup (it's a database of chains and will lose integrity). Similarly, you can't really copy all BUT something, same integrity issue. Deleting anything with Finder will definitely destroy the backup. Finder can't rebuild TM links.
Here is the dilemma. There is something you can try, but it might break the database of TM and you lose everything. And I don't know if it will work, or even if it can be done. Before you consider it, you need to ask yourself "Is the risk of that loss of all the "tons of vitally important personal info on there of my own from the last few years" less than the risk of keeping the sensitive data?"
If it's more important to delete the sensitive data than the risk to the "vitally important" data, you can use Finder to go through the backups, starting with the most recent one by date and working ONLY backward through the backups to delete the links to the file, one by one. So, for example, if you erased one of the sensitive files last week, you start with today, then yesterday, then the previous day. When the offending file appears in the backup, you delete it. Then the day before, and before that, back to when the file disappears from the backup because you are now before the creation date. But you have to start from the "newest" version. You have to go backward because that will be trimming off the most recent link only, and not chopping the chain in the middle, losing integrity. And you have to go in sequence, one at a time, to try to avoid loss of integrity. And you have to never have a Folder link instead of a file link, because if you delete the folder link, you break all the chains of all the items in the folder, destroying the database integrity. And there is no way to know which is which from Finder. So, it's a very, very, risky way to go.
Personally, I wouldn't do it, it's too risky, but only you can make the decision of what is more important to you, the "vital" data or this "Sensitive" data. If you try this, just be prepared for the fallout if the entire backup goes awry. Don't say I didn't warn you. Don't open TM in the middle of the process to 'check on how it's going.' The first thing TM does is an integrity check and if it sees what you have done, it will declare the backup unusable and everything will be gone. It could very well do that once you finish, too, which is the risk in doing it. You also mentioned mail in the first post, so if what you want to delete is a mail message, be aware that you don't know how they are stored in Thunderbird and deleting something from the outside may well destroy the integrity of the Thunderbird data as well. So even if TM lets you do this, TB may well not. But maybe I misunderstood the reference to Thunderbird. If TB works the way most emails work, the message header may be in multiple locations, the body of text in another and any attachments (including images as part of headers/footers/signatures) in yet another, linked in a database so that TB can glue them together again for you to view. So, to delete a mail message you would need to know the database reference for it, the header, the addresses, and any and all attachments. And you would have to delete it in such a way that the database for TB is refreshed to not show that it has lost integrity.
BTW, you should be aware that if what these sensitive files are are, in fact, emails, the email provider has copies on their servers, no matter what you do. And the sender/receiver(s) of these emails may well have copies, both in their mail system and in any backups they may have made. So, that's another factor to consider.
I RECOMMEND YOU DO NOT DO IT.
But it's up to you. Only you know why this sensitive data is sensitive. Frankly, if these sensitive files are that critical, I'd destroy the drive and start over, vital data or not. Or I'd try to recover the vital data, then destroy the drive. The risk there is that you miss some vital files and don't realize it until after the drive is destroyed. And by "destroy" I mean disassemble the drive, remove the platters and shatter each one with a hammer. Finder can read the links and get to the real files for the vital data, so you could use it to find the vital data, copy it and paste it to a safe location, one by one. The same dilemma faces you in this scenario for the Thunderbird email, you would have to find a way to find all the parts of the vital messages and reassemble them to recover to a safe location.
One other think you could try is encrypting the backup or encrypting the whole TM drive. I don't know if you can encrypt the backup after the fact, but you can research that. Then put a ridiculously hard to guess password on it and only YOU can get to it. The data isn't erased, but pretty unreadable to all but the really serious agents (think intelligence forces for that). Nothing is perfectly secure, except maybe the hammer approach.